Find a value c in the interval [0,2] such that f(c)is equal to the average value.
To find a value c in the interval [0,2] such that f(c) is equal to the average value, you need to follow these steps:
1. Evaluate the average value of the function f(x) over the interval [0,2].
- To do this, you need to find the definite integral of f(x) over the interval [0,2] and divide it by the length of the interval, which is 2-0 = 2.
2. Find the definite integral of f(x) over the interval [0,2].
- To find the definite integral, you need to know the function f(x) and integrate it over the interval. The definite integral of f(x) from a to b is denoted as ∫[a,b] f(x) dx.
- If you provide the function f(x), I can help you find its definite integral.
3. Once you have evaluated the average value and found the definite integral, set f(c) equal to the average value and solve for c.
- Replace f(c) with the average value you found in step 1 and solve the equation for c.
Note: Without knowing the specific function f(x), it is not possible to provide an exact value for c.
To find a value c in the interval [0,2] such that f(c) is equal to the average value, we need a function f(x) and the average value of that function over the interval [0,2].
Could you please provide the function f(x) for which we need to find the value c?